► Speed and Distance sums
1) Azman can paint a wall mural in 3 hours. Rosli can paint the same wall mural in 2 hours. If they work together, how long will they take to paint the wall mural?
Ans :- They will take 1 1⁄5 h.
2) The distance between Point A and Point Z is 12 km. At 7.32 a.m., Eric cycled from Point A to Point Z at 8 km/h. At the same time, Joshua lEft Point Z and cycled towards Point A at 12 km/h.
(a) Find the distance that each of them had travelled when they passed each other
(b) At what time did the two of them meet?
Ans :- a) Eric travelled 4.8 km and Joshua travelled 7.2 km
b) Two of them met at 8.08 am.
3) Martin drove his car from Singapore to Muar. He travelled at 90 km/h for the first 1 ½ hours, rested for 30 minutes and increased his speed by 30 km/h for the next 1 hour to complete the remaining journey. Find the average speed of his car for the whole journey.
Ans :- 85 km/h.
4) Town X and Town Y are 665 km apart. At 11 a.m., Mrs Poh left Town X for Town Y travelling at a constant speed. At the same time, Mrs Soh left Town Y for Town X travelling at a constant speed which was 18 km/h faster than Mrs Poh. Find the average speed of Mrs Poh if they met at 2.30 p.m.
Ans :- 86 km/h.
5) Frank was travelling from Town A to Town B at a uniform speed. He drove past Tom who was travelling at a uniform speed of 84 km/h in the opposite direction. One and a half hours later, Frank reached Town B while Tom was still 39 km away from Town A. If Frank took 4 hours to travel to Town B from Town A, what was the distance between the two towns?
Ans :- Distance between the two towns is 264 km.
6) Kim started driving at 8 a.m. She drove from Happy Town to Sunny Town at an average speed of 84 km/h for 2 hours and 35 minutes. She then continued to drive to Vibrant Town at an average speed of 78 km/h. She reached Vibrant Town at 12 noon. What was her average speed for the whole journey?
Ans :- Her average speed was 81.87 km/h.
7) Mike and Mary worked together to paint a house. During the process, Mike took 9 days off and Mary took 2 days off. However, they were not absent on the same days. If they had done the job alone, Mickey would have taken 15 days and Mary would have taken 18 days. How long did Mike and Mary take to finish painting the house?
Ans :- 14 days.
8) A group of painters are painting classrooms. If they paint 6 classrooms per day, they will be able to complete 1 day ahead of schedule. If they paint 4 classrooms per day, they will be 2 days behind schedule. how many classrooms are there?
Ans :- There are 36 class rooms.
9) There is a block of 100 flats. Ah Huat, a painter, paints one flat each month from January to November. The flats are painted in the same order and Ah Huat takes a holiday every December. If my flat was painted in May 2004, which month and year will it be painted next?
Ans :- Next it will be painted in June, 2013.
10) Jean and Kate drove at uniform speeds from Happy Town to Beach Town. Jean drove at 60 km/h. Kate drove at 20 km/h slower than Jean. Kate reached Beach Town 45 minutes later than Jean.
(a) What was the distance between the two towns?
(b) How many hours did Kate take to cover the journey? (Give your answer in decimal)
Ans :- a) 90 km
b) 2.25 h
11) Rachel and Dan were driving at uniform speeds towards each other. Rachel was driving at 60 km/h. At 3.30 p.m., both of them were 488 km apart.
The two only passed each other at 7.30 p.m.
At what speed was Dan travelling?
Ans :- 62 km/h.